Differentiate sin 2x with respect to e cos x
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Differentiate sin^2x with respect to e^cos x
Answered by admin @
we have to differentiate sin²x with respect to .
step1 : differentiate, y = sin²x with respect to x,
dy/dx = d(sin²x)/dx
= 2sinx × d(sinx)/dx
= 2sinx × cosx
hence, differentiation of sin²x with respect to x is dy/dx = 2sinx.cosx
step2 : differentiate z = e^{cosx} with respect to x,
dz/dx = d(e^{cosx})/dx
= e^{cosx} × d(cosx)/dx
= e^{cosx} × (-sinx)
= -sinx . e^{cosx}
hence, differentiation of e^{cosx} with respect to x is dz/dx = -sinx . e^{cosx}
step3 : now dividing (dy/dx) by (dz/dx), we get differentiation of sin²x with respect to e^(cosx).
i.e., (dy/dx)/(dz/dx) = (2sinx.cosx)/(-sinx.e^{cosx})
or, dy/dz = -2cosx/e^{cosx}
hence, differentiation of sin²x with respect to e^(cosx) is -2cosx/e^{cosx}
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